Trace Expressions and Associated Limits for Non-Equilibrium Casimir Torque

TL;DR

This paper develops trace-based formulas for Casimir torque in non-equilibrium settings, deriving bounds on maximum torque for single objects and extending the formalism to multiple particles, with implications for nanotechnology and materials science.

Contribution

It introduces a novel trace formalism for Casimir torque and derives bounds on maximum torque for isotropic objects out of equilibrium, extending to multiple bodies.

Findings

Maximum torque scales with body volume in different regimes.

Achievable torque is within an order of magnitude of optimized designs.

Formalism can be extended to multiple interacting bodies.

Abstract

We exploit fluctuational electrodynamics to present trace expressions for the torque experienced by arbitrary objects in a passive, non-absorbing, rotationally invariant background environment. Specializing to a single object, this formalism, together with recently developed techniques for calculating bounds via Lagrange duality, is then used to derive limits on the maximum Casimir torque that a single object with an isotropic electric susceptibility can experience when out of equilibrium with its surrounding environment. The maximum torque achievable at any wavelength is shown to scale in proportion to body volumes in both subwavelength (quasistatics) and macroscopic (ray optics) settings, and come within an order of magnitude of achievable torques on topology optimized bodies. Finally, we discuss how to extend the formalism to multiple bodies, deriving expressions for the torque experienced by two subwavelength particles in proximity to one another.